Thermocapillary flow and natural convection in a melt column with an unknown melt/solid interface

A vertical melt column set up between an upper heating rod and a lower sample rod, i.e. the so-called halfzone system, is a convenient experimental tool for studying convection in the melt in floating-zone crystal growth. In order to help understand the convection observed in the melt column, a computer model has been developed to describe steady state, axisymmetrical thermocapillary flow and natural convection in the melt. The governing equations and boundary conditions are expressed in general non-orthogonal curvilinear co-ordinates in order to accurately treat the unknown melt/solid interface as well as all other physical boundaries in the system. The effects of key dimensionless variables on the following items are discussed: (1)convection and temperature distribution in the melt; (2) the shape of the melt/solid interface; (3) the height of the melt column. These dimensionless variables are the Grashof, Marangoni and Prandtl numbers.     

基于黏弹性的微注射成型流动模拟

应用有限元方法研究了微注射成型中瞬态、可压缩、非牛顿熔体流动的黏弹性对流动前沿及流动平衡的影响。基于Phan-Thien-Tanner模型建立了熔体流动的本构方程,利用Hele-Shaw假设和简化建立了瞬态、可压缩、非牛顿熔体流动的连续性方程、动量方程、能量方程;为了有效地描述微注射成型的尺寸效应,采用了边界滑移和表面张力边界条件。通过分部积分和待定系数法导出了带有边界信息的变分方程和求解应力分量的半解析公式,构造了有限元离散求解及超松驰迭代算法。模拟结果表明:熔体的黏弹性对浇口附近的压力和后续的熔体流动前沿有重要影响;与黏性模型相比,黏弹性模型可以控制模拟压力的快速增长,减少不同型腔之间的充填差异,与短射实验结果也更吻合。     

Simulation and experimental analysis of melt pool evolution in laser engineered net shaping

In this work, the evolution of melt pool under single-point and single-line printing in the laser engineered net shaping (LENS) process is analyzed. Firstly, the basic structure of the melt pool model of the LENS process is established and the necessary assumptions are made. Then, the establishment process of the multi-physical field model of the melt pool is introduced in detail. It is concluded that the simulation model results are highly consistent with the online measurement experiment results in terms of melt pool profile, space temperature gradient, and time temperature gradient. Meanwhile, some parameters, such as the 3D morphology and surface fluid field of the melt pool, which are not obtained in the online measurement experiment, are analyzed. Finally, the influence of changing the scanning speed on the profile, peak temperature, and temperature gradient of the single-line melt pool is also analyzed, and the following conclusions are obtained: With the increase in scanning speed, the profile of the melt pool gradually becomes slender; The relationship between peak temperature and scanning speed is approximately linear in a certain speed range; The space temperature gradient at the tail of the melt pool under different scanning speeds hardly changes with the scanning speed, and the time temperature gradient at the tail of the melt pool is in direct proportion to the scanning speed.     

Fingerprinting the processing behavior of polyethylenes from transient extensional flow and peel experiments in the melt state

The flow curves of linear (linear-low and high density) and branched polyethylenes are known to differ significantly. At increasing shear rates, the linear polymers exhibit a surface melt fracture or sharkskin region that is followed by an unstable oscillating or stick-slip flow regime when a constant piston speed capillary rheometer is used. At even higher shear rates, gross melt fracture appears. Unlike their linear counterparts, branched polyethylenes rarely exhibit sharkskin melt fracture and although gross melt fracture appears at high shear rates there is no discontinuity in their flow curve. The various flow regimes of these two types of polyethylenes are examined by performing experiments in the melt state using a unique extensional rheometer (the SER by Xpansion Instruments) that is capable of performing accurate extensional flow and peel experiments at very high rates not previously realized. The peel strength curves of these linear and branched polyethylenes exhibit all of the distinct flow regimes exhibited in their respective flow curves, thereby providing a fingerprint of their melt flow behavior. Moreover, these extensional flow and peel results in the melt state provide insight into the origins and mechanisms by which these melt flow phenomena may occur with regard to rapid tensile stress growth, melt rupture, and adhesive failure at the polymer wall interface.     

A numerical study of heat transfer during flow of melt in a cylindrical mould

A numerical analysis of transient heat transfer during the flow of a melt in a cylindrical mould is presented. The analysis includes thermal resistance at the melt-mould interface, and axial conduction inside both melt and mould. Energy equations are formulated in a domain that expands continuously due to the advance of the melt inside the empty mould, and solved by the finite difference method using a time-stepping procedure. Calculations are compared to existing analytic results. It is found that axial conduction in the melt can significantly influence the rate of heat loss from the flowing melt, and that analytic approximations, which neglect axial conduction, may give erroneous predictions for the rate of heat loss.     

Effect of Microturbulent Flow on Gallium Crystal Growth from the Melt

The results of experiments on gallium crystal growth under conditions of microturbulent flow in the melt in a nonuniform vibration field are discussed. The vibration field in the conducting melt is generated by superposing profiled constant and oscillating magnetic fields. Among the features of the flow is the onset of intense small-scale turbulent flow which homogenizes the heat and concentration fields in the melt in the neighborhood of the growing crystal. High values of the transport coefficients, in particular, the effective thermal conductivity and diffusion coefficients, which ensure a high degree of supercooling of the melt in the neighborhood of the crystallization front, and a kinetic mechanism of single-crystal growth are recorded.     

From melt flow index to rheogram

A knowledge of the complete flow curve or rheogram of a polymeric melt depicting the variation of the melt viscosity over industrially relevant range of shear rate and temperature is essential in the design of polymer processing equipment, process optimization and trouble-shooting. These data are generated on sophisticated rheometers that are beyond the financial and technical means of most plastics processors. The only flow parameter available to the processor is the melt flow index of the material. In the present work, a method has been proposed to estimate the rheograms of a melt at temperatures relevant to its processing conditions with the use of a master curve, knowing the melt flow index and glass transition temperature of the material. Master curves that coalesce rheograms of different grades at various temperatures have been generated and presented for low density polyethylene, high density polyethylene, polypropylene, polystyrene and styrene-acrylonitrile copolymer.     

Effect of Thermocapillary Forces on the Initial Section of a Melt Film

The previous analysis of fields near the upper triple point of the floating–zone melting process is supplemented by the analysis of thermocapillary forces on the melt surface. It is shown that the effect of these forces is large in the general case, and a melt film with a macroscopic radius of curvature may be formed only if the temperature gradient over the melt surface and thermocapillary forces are small; in this case, the angular coordinates of the melt–film cross section are also small.     

液晶高分子-各向异性流体挤出拉伸分岔研究

应用共转导数型本构方程研究了液晶高分子纺丝挤出过程的拉伸黏度,应用计算机符号运算软件 Maple得出解析表达式,拉伸黏度与拉伸率之间关系(随剪切速率变化)表明存在分岔现象,得出拉伸黏度显著高于相应的剪切黏度,解释了液晶高分子熔体挤出时不发生挤出胀大的物理机制．     

Imaging and analysis of wave type interfacial instability in the coextrusion of low-density polyethylene melts

This report covers experimental studies and numerical modelling of interfacial instability in the bi-layer coextrusion flow of two low-density polyethylene melts. Melt streams are converged at an angle of 30° to a common die land. Melt stream confluence was observed in two coextrusion die arrangements. In one die design, which we term ‘bifurcated’ the melt stream is split by a divider plate in the die after being delivered from a single extruder. In the other design melt streams are delivered to a die from two separate extruders. In each die design melt flow in the confluent region and die land to the die exit was observed through side windows of a visualization cell. Velocity ratios of the two melt streams were varied and layer thickness ratios producing wave type interfacial instability determined for each melt for a variety of flow conditions. Stress and velocity fields in the coextrusion arrangements were quantified using stress birefringence and particle image velocimetry techniques.     

气体辅助注射成型过程动力学分析

基于气体穿透机理和Hele-Shaw流动模型,对管状模腔中气体冲破熔体前沿形成中空制品气辅成型过程进行了研究,推导出反映充模流动压力梯度比、非牛顿幂率指数等影响因素与计算表层熔体厚度比之间关系的数学公式,建立了熔体前沿和气体前沿速度与位移演化关系的数学模型,分别得出了牛顿流体和非牛顿流体选取不同影响参数时熔体前沿和气体前沿速度、位移的演化曲线.模拟结果表明,所建数学模型能较好的反映熔体前沿和气体前沿速度、位移演化关系.在气体冲破熔体前沿以前,气体接近匀加速运动,前沿位移梯度逐渐增加;熔体前沿的速度几乎保持不变,位移随时间接近线性增长.当气体冲破熔体前沿时,熔体和气体前沿的速度和位移均急速上升.     

A finite element method for analysis of fluid flow,heat transfer and free interfaces in Czochralski crystal growth

A finite element algorithm is presented for simultaneous calculation of the steady state, axisymmetric flows and the crystal, melt/crystal and melt/ambient interface shapes in the Czochralski technique for crystal growth from the melt. The analysis is based on mixed Lagrangian finite element approximations to the velocity, temperature and pressure fields and isoparametric approximations to the interface shape. Galerkin's method is used to reduce the problem to a non-linear algebraic set, which is solved by Newton's method. Sample solutions are reported for the thermophysical properties appropriate for silicon, a low-Prandtl-number semiconductor, and for GGG, a high–Prandtl–number oxide material. The algorithm is capable of computing solutions for both materials at realistic values of the Grashof number, and the calculations are convergent with mesh refinement. Flow transitions and interface shapes are calculated as a function of increasing flow intensity and compared for the two material systems. The flow pattern near the melt/gas/crystal tri-junction has the asymptotic form predicted by an inertialess analysis assuming the meniscus and solidification interfaces are fixed.     

Melting of horizontal ice layer from above by combined effect of temperature and concentration of aqua-solvent

This paper is concerned with the melting of horizontal ice layer from above by aqua-solvent with low solidification point. The solute used in this experiment are Sodium chloride NaCl, Calcium chloride CaCl₂, Magnesium chloride MgCl₂, and Urea CO(NH₂)₂- The upper surface of aqua-solvent melt layer is heated by an infrared lamp, whose temperature is in the range of about 8 ?C to 40 ?C. The ice layer located under the aqua-solvent melt layer melts greatly by a combined effect of both thermal energy and chemical reaction, and the typical temperature distribution in both aqua-solvent and ice layer is examined. The relation between melt amount of ice layer per unit temperature gradient and mean concentration in aqua-solvent melt layer was obtained.     

Mechanism of gross melt fracture elimination in the extrusion of polyethylenes in the presence of boron nitride

The mechanism by which the addition of a small amount of boron nitride into a polyethylene eliminates gross melt fracture is elucidated. Simple elongational viscosity measurements at high rates revealed that the presence of boron nitride decreases the extensional viscosity of polyethylenes. The extensional rates at which these effects are present were found to be about the same with those at which gross melt fracture is obtained (calculated from Cogswells analysis). Thus, it can be argued that the well dispersed boron nitride particles decrease extensional stresses that are responsible for gross melt fracture and/or their presence dissipate the release of energy resulting from isolated rupture or slip planes within the melt originating at the entrance to the capillary.     

熔喷双槽形喷嘴气体射流流场初探

在熔喷非织造布加工中,气体射流作为工作介质使聚合物熔体实现拉伸,气体射流流场的研究对熔喷气流拉抻数学模型研究非常重要。熔喷双槽形喷嘴形成的流场可以看作两股平面射流的合成。从单个点涡的性质出发,研究了涡偶的性质和涡偶代替射流的可行性。研究表明,在喷丝孔轴线附近,涡偶和射流的速度分布趋势相同,且有比较相近的速度分布,从而说明以涡偶代替射流是可行的。在此基础上,用两个涡偶分别代替两股射流,然后进行合成,推导出两股射流合成后速度分布的理论公式,该公式的计算结果与实验结果吻合较好。将该公式引入熔喷气流拉伸数学模型,预测出的纤维直径与采用经验公式时的预测结果几乎完全相同。结果表明,应用涡偶代替射流推导出的气流速度分布公式能够较好地描述熔喷双槽形喷嘴气体射流流场,可以用于完善熔喷气流拉伸数学模型。     

Numerical simulation of titanium dissolution in the aluminum melt and synthesis of an intermetallic compound

Titanium dissolution in the aluminum melt and synthesis of an intermetallic compound at constant temperature and pressure are numerically simulated by the molecular dynamics method. Owing to titanium dissolution, the TiAl₃ intermetallic compound is formed near the interface between the titanium crystal and aluminum melt. Based on the theory of weak solutions, a mathematical model of titanium dissolution in the aluminum melt is constructed. Dependences of the diffusion coefficient, equilibrium concentration of titanium, and dissolution rate on temperature are obtained.     

A Study of Magma Flows in the Case of Non-Equilibrium Diffusion of Water in the Melt

All volcanic eruptions are accompanied by the degasification of the magma, which results in the growth of gas bubbles in the silicate melt. The number and growth rate of the bubbles determine the character of the eruption. When the free-gas concentration is low, the eruption is weak and takes a short time. At high concentrations, the melt is fragmented and a gas-particle mixture is formed. This results in the catastrophic intensification of the eruption. In this study, for describing the magma flow in a volcano conduit with account for the mass transfer between the bubbles and the melt, we construct models in which the conduit magma flow is considered simultaneously with the dynamics of gas-bubble growth in the melt. The models describe the magma eruptions with equilibrium or weak growth of the bubbles and also with a moderate rate of bubble growth, which is more typical of volcanic systems. Using the models constructed, an intense steady-state eruption and the problem of the evolution of the eruption to the steady-state regime after the rupture of a plug near the top of the conduit are considered. The effect of gas diffusion on the intensity and duration of the eruption is indicated.     

Freezing of a thermite melt injected into an annular channel experiments and recalculations

The analysis of hypothetical accidents of liquid metal cooled fast breeder reactors (LMFBR) shows that the reactor core can under certain circumtances undergo melting. The movement and freezing behavior of the molten core material are of primary importance for the subsequent course of the accident.

To investigate the characteristics of freezing and crust formation of a melt penetrating into cold structure, a series of out-of-pile experiments was performed using a simple cylindrical geometry. In the experiments the molten fuel was simulated by a thermite melt that was formed by the reaction of iron oxide and aluminum and was forced into a freezing channel. The movement of the melt was observed by X-ray cinematography and on-line instrumentalation. Post-test examination supplied information about the distribution of the relocated material and the formation of the crusts. The tests were then analyzed with the multicomponent computer code BUCOGEL. The test results show that the freezing behavior of the thermite melt is comparable to that of a uranium oxide/stainless steel mixture as used in in-pile tests conducted in similar geometry. The results of the thermite tests are therefore regarded as suitable to validate the relocation and freezing modules of computer codes describing whole-core accidents.     

用PSM模型模拟聚合物熔体的长口模挤出胀大

 以作者提出的模拟黏弹流体挤出胀大流动的方法为基础，计算了 IUPAC-LDPE熔体经过长圆形口模的挤出胀大. 计算结果同文献的报道 基本一致，表明作者提出的方法适于黏弹聚合物熔体的挤出胀大模拟.     

Gas displacement of polymer melts in a cylinder: Experiments and viscoelastic simulations

Series of isothermal gas-displacement of a polystyrene melt in a circular cylinder were performed. The experiments show an increase in the steady fractional coverage above a Newtonian level (m = 0.6) at very low Deborah numbers, where the melt behaves like a diluted un-entangled system. At higher Deborah numbers, where the melt behaves as an entangled melt system, the steady fractional coverage decreases.